No clear winner. The survival gap is under 10 percentage points and the balanced-score gap is under 0.05, so neither SolvSRK nor the best baseline clears the win threshold. Either works — choose on cost, licensing, or integration effort. All verdicts →
Limit-cycle oscillator, mildly nonlinear; biological and circuit analog
Canonical benchmark implementation
Canonical RHS excerpt from the registered callable used for this benchmark cell. Expand it to verify the state equations; it is not a standalone runnable fixture.
def _vdpol_rhs(t, y, mu=1.0):
x, v = y
return np.array([v, mu * (1 - x**2) * v - x])
def rhs(t, y):
return _vdpol_rhs(t, y, mu=1.0)Canonical RHS excerpt captured from the same registered callable used for the published benchmark. Frozen closure values are summarized below; helper imports and solver settings are intentionally omitted.
Fingerprint
Spread: low
Default noise: low
Recommendation snapshot
Clean best: SciPy Radau
Noisy best: SciPy LSODA
Coverage
14 solver arms · clean + 5 noise levels
Ranked on survival, precision, and speed
20 seeds/cell default · 14 arms · TRL 4–5 · simulation-lab validated · this page: Van der Pol (mu=1) (van-der-pol-mu-1)
Governed SolvTune benchmark freeze; per-arm medians only. RHS definitions and raw trial rows are not published.
Self-reported by Resonix Labs · not independently verified
Pick an objective and a noise level to rank all arms on survival, median SCD, median nfev, and median wall time. Medians across seeds.
Objective
Best overall trade-off of survival, precision, and speed.
Noise level
| # | Solver | Survival | SCD | nfev | Wall | Score |
|---|---|---|---|---|---|---|
| 1 | SciPy RadauSciPy | 100% | 10.2 | 8,974 | 179 ms | 0.861 |
| 2 | SolvSRK | 100% | 9.2 | 5,206 | 12 ms | 0.838 |
| 3 | SciPy DOP853SciPy | 100% | 9.1 | 1,838 | 12 ms | 0.835 |
| 4 | Vern9external | 100% | 9.0 | 1,570 | 4.47 s | 0.834 |
| 5 | Vern7external | 100% | 8.5 | 1,782 | 4.52 s | 0.822 |
| 6 | SciPy RK23SciPy | 100% | 8.2 | 13,055 | 114 ms | 0.815 |
| 7 | Tsit5external | 100% | 7.4 | 2,280 | 1.05 s | 0.796 |
| 8 | SciPy RK45SciPy | 100% | 7.3 | 2,198 | 15 ms | 0.792 |
| 9 | SciPy LSODASciPy | 100% | 6.7 | 1,183 | 5 ms | 0.778 |
| 10 | CVODE Adamsexternal | 100% | 6.4 | 880 | 17 ms | 0.771 |
| 11 | SciPy BDFSciPy | 100% | 6.4 | 2,961 | 99 ms | 0.771 |
| 12 | FBDFexternal | 100% | 6.1 | 2,155 | 5.27 s | 0.763 |
| 13 | CVODE BDFexternal | 100% | 5.9 | 1,222 | 20 ms | 0.759 |
| 14 | TRBDF2external | 100% | 4.0 | 10,213 | 5.82 s | 0.714 |
At Clean, best balanced arm is SciPy Radau · SolvSRK survival 100%, SCD 9.2.
Values are medians across seeds, measured by Resonix Labs on Resonix hardware and not independently verified; nfev and wall are on reference lab hardware (indicative). Under injected noise only SolvSRK and the SciPy arms are run. How we measure accuracy → · Verification status →
SolvScout · free
This page shows one published benchmark cell. SolvScout fingerprints your ODE, compares it to the full corpus, and recommends a solver with the same survival / precision / speed ranking you see here — including when a SciPy arm wins.
SolvSRK · 30-day trial
SolvSRK is the stiffness-adaptive integrator behind the SolvSRK column in these tables. Create an account, activate a machine, and take a 30-day trial — same binary you'd ship after purchase.
Replace the access date. Pin the freeze ID and library versions when comparing against a later export. Cite it as what it is — a self-reported vendor benchmark, not an independently verified result. The note field says so; please keep it.
@misc{resonix_evidence_van_der_pol_mu_1_2026,
title = {Resonix Evidence Portal: Van der Pol (mu=1)},
author = {{Resonix Labs (Canada) Inc.}},
year = {2026},
howpublished = {\url{https://resonix.tech/evidence/problems/van-der-pol-mu-1}},
note = {Self-reported vendor benchmark; internally generated by Resonix Labs and not independently verified. Accessed YYYY-MM-DD. Freeze 2026-08-13; libsolvsrk 2.3.0; SciPy 1.14.}
}TRL 4–5 · simulation-lab validated · 398 problems · 14 solver arms · clean + 5 noise levels
Freeze: 2026-08-13 · scipy 1.14 · libsolvsrk 2.3.0 · Methodology
Self-reported by Resonix Labs · not independently verified · Verification status